Identification of cotton properties to improve yarn count
quality by using regression analysis
Muhammad Amin1, Muhammad Ammanullah2 and Atif Akbar3
Abstract
The study reveals the identification of raw material characteristics towards yarn count variation
by using statistical techniques. Regression analysis is used to meet the objectivity. Stepwise
regression is used for model selection and, coefficient of determination and mean squared error
(MSE) criteria are used to isolate the contributing factors of cotton properties for yarn count.
Statistical assumptions of normality, autocorrelation and multicollinearity are evaluated by using
probability plot, Durbin Watson test, variance inflation factor (VIF), and then model fitting is
carried out. It is found that, INV (Invisible), Nep (Nepness), RD (Grayness), TR (Trash) and UI
(Uniformity Index) are the main contributing cotton properties for yarn count variation. The
results are also verified by Pareto chart and the main factor for yarn count quality is TR (cotton
trash).
Key words: Autocorrelation, Cotton Properties, Regression analysis, Stepwise regression, Yarn
count; Yarn quality.
1 Introduction
Textile products are manufactured for daily uses and ceremonial purposes. Products such as
ropes, wicks and sailing cloth have been a part of our civilization since years to years. Yarn
holds a principal position for manufacturing textile products which is manufactured on the basis
of cotton fibers. Yarn is used for manufacturing fabrics which is used in apparel, home textile
furnishing and industrial products. Apparel includes trousers, shorts, shirts and jeans. Yarn is an
input for knitters who produce fabric and demand high quality of yarn to produce fine quality of
fabric.
Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
Email: ma_amin15@yahoo.com
2
Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
E-mail: aman_stat@yahoo.com
3
Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
Email: atifakbar@bzu.edu.pk
The textile industry contains different subunits, i.e., spinning, dying, weaving and knitting. There
are three methods for yarn manufacturing, cotton yarn is one of these and the most important
textile spinning production method. (Jackowski et al., 2002). Always knitter and weaver are
demanding a high quality of yarn for the textile products. Hard global competition, however
usually prevents turning yarn quality improvements into higher sales prices. Yarn is produced in
different counts which range from 10s, 20s, and 30s to 80s and above (where s stands for single).
These different counts of hank (a unit of length) yarn are used to produce different types and
quality of cotton cloth. The lower counts of yarn, below 40s, are used to produce lower quality
cotton cloth while the higher counts are used to produce higher quality segment of the cloth.
There is a relationship between the quality of raw materials and the end products. The lower the
quality of cotton fibers, the lower the quality of yarn produced. Cotton is the main natural fiber
which presents large variation in its properties (Majumdar and Majumdar, 2004; Price et al.,
2009). Physical properties of cotton affect the production efficiency and yarn quality. These
physical properties includes color, elongation, invisible, maturity ratio, micronair, moisture,
nippiness, fiber strength, trash, upper half mean length, uniformity index. High quality cotton
blends are superior with respect to properties such as length, fineness, elongation, brightness,
sufficiently mature and without any trash particles, and displaying a high capacity of spinning
consistency. Yarn English count for natural fiber (yarn count) is one of the important yarn
quality measuring parameter. Yarn count is very important for yarn count lea strength product
(CLSP) because yarn product with high CLSP produced good quality of cloth. Therefore
consistency in yarn count parameter is necessary for good quality of yarn. That’s why come to
the study the effect of input cotton properties on yarn count. In this research article, our objective
is to determine the most important cotton quality factors which affect the quality of yarn
regarding yarn count, by using regression analysis.
Koo and Suh (2005) have used a regression analysis to study the effect of fiber properties and
process parameters in the textile industry on yarn quality characteristics and found that fiber
length is the significant factor for all manufacturing process and these results are misleading due
to multicolinearity among independent variables. Ureyen and Kadoglu (2007) used a linear
regression models to predict the cotton yarn properties on the basis of fiber properties. They
have studied different yarn characteristics separate on fiber physical properties and found that
these properties have great affect on all yarn characteristics. Üreyen and Gürkan (2008) used
artificial neural network (ANN) and regression models to predict the yarn tensile properties and
find that fiber strength and elongation are the most significant factors for yarn tensile properties.
Also they compared the ANN and regression method on the basis of Adjusted  R 2 and MSE
and found that ANN is more powerful than regression method. The same study then applied by
Üreyen and Gürkan (2008) to predict the yarn hairiness and unevenness and same conclusions
are drawn. Majumdar et al (2008) are used to test the accuracy of two computing approaches i.e.
ANN and neural-fuzzy system to forecast the unevenness of ring spun yarns and compares these
two methods with regression on the basis of cotton properties and yarn count. They have found
that these two computing approaches are better and consistent than linear regression method.
Same study were conducted by Nurwaha and Wang (2009) on strength of rotor yarn. Fattahi et
al. (2010) have used robust regression to study the fiber factors for yarn quality characteristics.
Bo (2010) applied a multiple regression and neural network model to predict the cotton yarn
hairiness on the basis of spinning process parameters i.e. roller speed (F), spindle speed (S), nip
gauge (N), back draft zone time (B), and roving twist (R). They have found that both methods
give reliable results. But they have not identified the most important spinning process parameters
for predicting the yarn hairiness. Lewandowski et al. (2010) conducted a comparative analysis of
ring spinning process by using regression analysis. Nurwaha and Wang (2012) predict textile
yarn quality characteristics on the basis of cotton physical properties and found that for yarn
quality count strength product (CSP) the most important factors are fiber strength elongation.
2. Materials and Methods
In this section we discuss variables of interest and data. Also we describe the statistical tools for
data analysis to explore the most important factors of yarn quality characteristics.
Data concerned to our study is obtained from the Colony Textile Mills (CTM) Multan, Pakistan.
Data is related to yarn quality characteristics i.e.
Yarn count (NEC) and cotton physical
properties of yarn product 40/1s. These cotton physical properties are given in the following
Table 1;
Table 1: Variables Description of fiber and yarn quality characteristics
Variable
Description
Unit
Symbol
Y
Yellowness
b+
A
ELG
Elongation
%
B
INV
Invisible
g
C
Maturity Ratio
MR
%
D
MIC
Micronaire
g
E
mm
Moist
Cotton Moisture
%
F
Nep
Nepness
g
G
RD
Grayness
rd
H
Str
Fiber Strength
g/tex
I
TR
Trash
g
J
UHML
Upper half mean length
mm
K
UI
Uniformity Index
%
L
Yc
Yarn Count
tex
Y
Where Y is the dependent (out put) and A to L, are independent variables (input parameters). In
Table 1, the term symbol is further used in regression model i.e. used for model selection.
Further details about yarn and cotton quality parameter may be found in (Lawrence, 2003).
2.1 Regression Analysis
Modeling yarn characteristics, is an important field of the textile spinning research. In modeling
regression analysis tools are very useful (Majumdar et al., 2008). These tools are very useful for
yarn quality improvement, because these tools quantify the relationship between yarn quality
characteristics and cotton properties. Also regression analysis provides the identification of
significant parameters for yarn quality characteristics and resultantly the quality of yarn.
2.2 Regression Model
To study the effect of cotton properties on yarn count quality we consider regression model
Y  X  
Where Y is a vector of response variable of dimension n  1 , X is the matrix of independent
variables of dimension n  p  , and

is the matrix of unknown parameters of
dimension  p  1 , and  is random error of dimension n 1 , and follow a normal distribution
with zero mean and constant error variances.
In our study, we are concerning the yarn characteristics, i.e. yarn count, with its cotton as a input
parameters. The resulted model, using symbols for cotton properties, available in Table 1, is
given by
Y  0  1 A  2 B  3C  4 D  5 E  6 F  7G  8 H  9 I  10 J  11K  12 L 
Where Y is the dependent and A to L are the independent variables, p represents the number of
unknown parameters in regression model.
 0 is the intercept and  i s are the slope coefficients of independent variables.
The assumptions of the linear regression model includes normality, zero mean, constant variance
of the error term, no correlation among regressors, independence of the error term, etc. (Drapper
and Smith, 1998).
To validate these assumptions probability plot (normality), Durbin Watson
test (autocorrelation) and VIF for multicollinearity are calculated and inferences are drawn
accordingly. Detailed may be seen in (Drapper and Smith, 1998; Gujarati, 2003).
2.3 Stepwise Regression
Stepwise regression is used to identify important input (Trash, Fiber Strength, etc) are cotton
properties which contribute maximum determination of yarn count variation. To proceed for
model selection by stepwise regression, initially, we regress average yarn count on fiber strength
and note the results i.e. Adjusted- R 2 MSE and mallows Cp etc. In the next step, we regress
average yarn count on cotton Properties, fiber strength and micronaire (i.e, we add an other input
to the average yarn count) and note that the results as described above. The will continue until all
Cotton Properties are to be included in the model. The process is known as forward selection.
Similarly starting from the full model, and then removing the independent variable one by one is
known as backward elimination method. And we will select the model, which contains
maximum Adjusted-R2 and minimum MSE (Bingham and Fry, 2010; Kutner et al., 2005;
Paulson, 2007).
3 Results and Discussions
The results of stepwise regression for model selection is given as in Table 2.
Table 2: Models with largest adjusted R-squared for yarn count
MSE
R 2 (%)
Adjusted- Mallows
Cp
R 2 (%)
Included
Variables
0.0092
0.0106
0.0109
.
.
.
0.0306
0.0306
0.0306
76.7973
71.7519
72.5185
.
.
.
4.5455
4.5455
0.0000
69.9729
65.4745
64.4357
.
.
.
0.0000
0.0000
0.0000
CGHJL
CGHJ
CGHJK
.
.
.
L
K
Constant
0.7389
1.2916
2.9037
.
.
.
29.7826
31.5620
29.5930
In this analysis there are 1586 models fitted for yarn quality characteristic yarn count on
the basis of 12 cotton properties (as available in Table 1). The model which gives the largest
Adjusted- R 2 and minimum MSE values is the best fitted. By using stepwise regression for
model selection, the best model for yarn count includes variables C, G, H, J, and L (AdjustedR 2 = 69.97 and MSE = 0.0092) as shown in second row of the Table 2 above and corresponding
input parameters INV, Nep, RD, TR and UI.
After model selection for yarn count with input parameters INV, Nep, RD, TR and UI,
we then regress yarn count on these selected input parameters to identify the most important
input parameters. Following tables shows the regression analysis of the selected model.
Table 3: Analysis of variance (ANOVA) for yarn count model.
Source
Sum of
Squares
Df
Mean
Square
F-Ratio
p-value
Model
Residual
Total
R2= 76.79%
0.5170
0.1562
0.6732
5.0000
17.0000
22.0000
0.1034
0.0092
11.2500
0.0001
Adjusted-R2 = 69.97%
Durbin Watson = 1.2045 (p-value= 0.3343)
Table 4: Regression analysis for yarn count model.
Parameter
ˆ
S.E ( ˆ )
t-stat
p-value
VIF
Constant
INV
Nep
RD
TR
UI
24.7902
0.1815
0.0020
0.1548
0.1932
0.0248
2.6520
0.0468
0.0006
0.0282
0.0299
0.0129
9.3479
3.8803
3.1882
5.4794
6.4641
1.9227
0.0000
0.0012
0.0054
0.0000
0.0000
0.0714
2.0104
2.0240
2.2104
2.2083
1.5442
We fit a multiple linear regression model to describe the relationship between yarn count
and five input parameters. The equation of the fitted model is;
Y = 24.7902 + 0.1815 INV + 0.0020 Nep + 0.1548 RD + 0.1931 TR - 0.0248 UI
ANOVA results given in Table 3, indicate that the dependence of yarn count on selected input
parameters is significant. Now to identify which parameter is actually contributes maximum
variation to explain in yarn count quality, we move on Table 4 and observe that INV, Nep, RD,
and TR are significant (p < 0.05 in all these cases). But UI has no significant effect on yarn
count.
The Adjusted- R 2 (= 69.97 %) indicates the goodness of input parameters and shows about 70%
explanation in yarn count due to these input parameters. To validate the assumption of
independence of residuals, Durbin Watson statistic, assures the independence (p-value = 0.3343).
Also small VIF’s (i.e. VIF < 5) shows that all input parameters are independent to each other.
To check the normality of residuals, we draw a probability plot of residuals, which shows that
residuals follow normal distribution (Figure1).
Figure1: Probability plot for yarn count
Figure 2: Pareto plot for yarn count input parameters
From the Pareto plot (Figure 2), we found that the main factor which affects yarn count is the TR
(fiber trash). So for purchasing cotton, the higher concentration should be given to cotton trash,
i.e. for the high quality of yarn count, the spinner should prefer to purchase the cotton with
minimum trash.
4 Conclusion
We have studied material factors which affect on yarn quality characteristic, i.e. yarn count, by
using regression analysis. We regress yarn count on 12 independent variables (input parameters)
and select the regression model by stepwise regression under the assumption that the model is
best which have largest Adjusted  R 2 and minimum MSE. There are 1586 models fitted for
yarn quality characteristic and the best model to explain yarn count variation contains INV, Nep,
RD, TR and UI as explanatory variables. Statistical assumptions of the model are tested through
standard techniques and then applied regression analysis, having validation of assumptions.
The main factor for yarn count quality on the basis of cotton properties is TR (cotton trash) as
signified by t-test and Pareto chart. This indicates that lower the trash in cotton produced good
quality of yarn regarding yarn count. So spinner purchase and use the cotton with lower trash for
manufacturing good quality of yarn to satisfy their customers.
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